Stable Fuzzy Logic Control of Generalized van der Pol Oscillator

Abstract

This paper suggests the design of Takagi-Sugeno (T-S) fuzzy logic controllers (FLCs) to stabilize the generalized van der Pol oscillator as a representative nonconservative oscillator with nonlinear damping. The design is supported by the stability analysis in the sense of Lyapunov using the global invariant set theorem. A new stability analysis theorem is formulated to offer sufficient conditions for the stability of the fuzzy control system that consists of the van der Pol oscillator controlled by T-S FLCs. The simulation results show good fuzzy control system performance.